Vladimirov, Igor G.2026-07-022026-07-029781713872344https://hdl.handle.net/1885/733812284This paper is concerned with quadratic-exponential moments (QEMs) for dynamic variables of quantum stochastic systems with position-momentum type canonical commutation relations. The QEMs play an important role for statistical “localisation” of the quantum dynamics in the form of upper bounds on the tail probability distribution for a positive definite quadratic function of the system variables. We employ a randomised representation of the QEMs in terms of the moment-generating function (MGF) of the system variables, which is averaged over its parameters using an auxiliary classical Gaussian random vector. This representation is combined with a family of weighted L2-norms of the MGF, leading to upper bounds for the QEMs of the system variables. These bounds are demonstrated for open quantum harmonic oscillators with vacuum input fields and non-Gaussian initial states.This work is supported by the Australian Research Council grants DP210101938, DP200102945.6enPublisher Copyright: Copyright © 2023 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)moment-generating functionprobabilistic boundQuadratic-exponential momentquantum stochastic systemrandomised representation2023-07-0110.1016/j.ifacol.2023.10.11385184962260